A007291 Series expansion for rectilinear polymers on square lattice. (Formerly M4440)

7, 63, 254, 710, 1605, 3157, 5628, 9324, 14595, 21835, 31482, 44018, 59969, 79905, 104440, 134232, 169983, 212439, 262390, 320670, 388157, 465773, 554484, 655300, 769275, 897507, 1041138, 1201354, 1379385

Offset

2,1

References

V. B. Priezzhev, Series expansion for rectilinear polymers on the square lattice, J. Phys. A 12 (1979), 2131-2139.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=2..30.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

G.f.: (7 + 28x + 9 x^2 ) / ( 1 - x )^5.

a(n)=n(n-1)(11n^2-13n+3)/6 - T. D. Noe, Feb 09 2007

a(2)=7, a(3)=63, a(4)=254, a(5)=710, a(6)=1605, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Oct 17 2012

Mathematica

Table[(n(n-1)(11n^2-13n+3))/6, {n, 2, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {7, 63, 254, 710, 1605}, 40] (* Harvey P. Dale, Oct 17 2012 *)

Prog

(PARI) a(n)=n*(n-1)*(11*n^2-13*n+3)/6 \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Sequence in context: A167550 A304895 A161201 * A343137 A188226 A055405

Adjacent sequences: A007288 A007289 A007290 * A007292 A007293 A007294

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved